Higher Level assumes a lot of Junior Cert groundwork and never re-teaches it. It's usually the gaps here — not the hard topics — that quietly cost marks. Watch the intro, skim the sections you're shaky on, and check yourself as you go.
A quick run through the groundwork Higher Level takes for granted. If everything here already feels obvious, skip straight to Algebra 1.
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Section 1
Fractions, Decimals & Percentages
These three are the same idea wearing different clothes, and Higher Level swaps between them without warning. You need to move between them quickly — and be able to handle fractions by hand, because a lot of algebra is just fraction work with letters in it.
To add or subtract fractions you need a common denominator. To multiply, go straight across. To divide, flip the second one and multiply.
EXAMPLE Work out ⅔ + ¼
Common denominator of 3 and 4 is 12.
⅔ = 8/12 and ¼ = 3/12
8/12 + 3/12 = 11/12
Never add denominators. ⅔ + ¼ is not 3/7 — a classic slip under pressure.
Check yourself
Q1 Increase €48 by 15%
15% of 48 = 0·15 × 48 = 7·20 48 + 7·20 = €55·20
Faster: multiply by 1·15 in one step. Worth getting comfortable with — it's the backbone of Financial Maths later.
Q2 Write 0·375 as a fraction in its simplest form
0·375 = 375/1000 Divide top and bottom by 125 → 3/8
Q3 Work out ⅗ ÷ ¾
Flip the second and multiply: ⅗ × 4/3 = 12/15 = 4/5
Section 2
Negatives & Order of Operations
More Higher Level marks are lost to a stray minus sign than to any hard concept. Squaring negatives and subtracting brackets are the two places it goes wrong most often.
BIMDAS — Brackets, Indices, Multiplication/Division (left to right), Addition/Subtraction (left to right). Watch:(−3)² = 9 but −3² = −9. The brackets change everything.
EXAMPLE Simplify 5 − (2 − 7)
Brackets first: 2 − 7 = −5 5 − (−5) = 5 + 5 = 10
Subtracting a negative adds. Two minuses meeting always make a plus.
Take the root first, then the power — the numbers stay small and manageable.
Q3 Simplify (2x³)²
The power hits both parts: 2² = 4 and (x³)² = x⁶ → 4x⁶
Forgetting to square the 2 is the most common error here.
Section 4
Rearranging Formulae
You'll be asked to make a variable the subject constantly — in calculus, in trigonometry, and every time you use the Formulae & Tables booklet. Whatever you do to one side, do to the other.
EXAMPLE Make r the subject of A = πr²
Divide both sides by π: A/π = r² Square root both sides: r = √(A/π)
Check yourself
Q1 Make x the subject of y = 3x − 7
y + 7 = 3x → x = (y + 7)/3
Q2 Make h the subject of V = ⅓πr²h
Multiply both sides by 3: 3V = πr²h Divide by πr²: h = 3V/(πr²)
Section 5
Rounding & Scientific Notation
Nearly every exam question tells you how to round. Ignoring that instruction throws away marks you've already earned by doing the maths correctly.
Significant figures start from the first non-zero digit. Scientific notation is a × 10n where 1 ≤ a < 10. Golden rule: round only at the very end. Rounding halfway through drags your final answer off.
Check yourself
Q1 Write 0·004071 to 2 significant figures
First significant figure is the 4. Next is 0; the digit after is 7, so round up → 0·0041
Q2 Write 38 500 in scientific notation
3·85 × 104
Section 6
Your Exam Toolkit
📗 The Formulae & Tables booklet. You're given one in the exam and you can't bring your own. Get a copy now and learn what's actually in it — a surprising number of marks are lost hunting for a formula that was on page 9 all along.
🔢 Your calculator. Know your own model properly — fractions, surds, stats mode, and degrees vs radians. Exam day is a bad time to find out where a button lives.
Comfortable with all of the above? You're ready to start.